Macdonald’s Identities and the Large N Limit of Y M2 on the Cylinder
نویسنده
چکیده
The purpose of this paper is to determine the large N asymptotics of the free energy FN (a, U |A) of Y M2 (two-dimensional Yang Mills theory) with gauge group GN = SU(N) on a cylinder where a is a so-called principal element of type ρ. Mathematically, FN (U1, U2|A) = 1 N2 log HGN (A/2N, U1, U2) is the central heat kernel of GN . We find that FN (aN , UN |A) ∼ N A Ξ(dθ, dσ) where Ξ is an explicit quadratic functional in the limit distribution dσ of eigenvalues of UN , which depends only on the integral geometry of SU(2). The factor of N appears to contradict some predictions in the physics literature on the large N limit of Y M2 on the cylinder (due to Gross-Matytsin, Kazakov-Wynter others).
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متن کاملMacdonald ’ s Identities and the Large N Limit of YM 2 on the Cylinder Steve
The purpose of this paper is to determine the large N asymptotics of the free energy FN (a, U |A) of YM2 (two-dimensional Yang Mills theory) with gauge group GN = SU(N) on a cylinder where a is a so-called principal element of type ρ. Mathematically, FN (U1, U2|A) = 1 N2 logHGN (A/2N,U1, U2) is the central heat kernel of GN . We find that FN (aN , UN |A) ∼ N A Ξ(dθ, dσ) where Ξ is an explicit q...
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